CN111366905A - Space micro-motion group target multi-channel blind source separation method - Google Patents

Space micro-motion group target multi-channel blind source separation method Download PDF

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CN111366905A
CN111366905A CN202010282510.8A CN202010282510A CN111366905A CN 111366905 A CN111366905 A CN 111366905A CN 202010282510 A CN202010282510 A CN 202010282510A CN 111366905 A CN111366905 A CN 111366905A
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CN111366905B (en
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陈如山
丁大志
樊振宏
叶晓东
何姿
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/415—Identification of targets based on measurements of movement associated with the target
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

The invention discloses a space micro-motion group target multi-channel blind source separation method, which solves the multi-channel blind source separation problem of a micro-motion warhead group target and requires that the number of received echoes of a radar is more than or equal to the number of warheads in the group target; firstly, a radar transmits a single-frequency pulse signal to obtain a plurality of micro-motion echoes of n warheads; randomly setting a positive definite mixed matrix to obtain an n-dimensional mixed signal, and preprocessing the n-dimensional mixed signal; establishing a fourth-order cumulant matrix according to the processed mixed signals, performing joint diagonalization, and establishing a target function; establishing a Givens rotation matrix, and finding a unitary matrix which meets a target function, namely a de-mixing matrix; thereby reconstructing the source signal. According to the method, a fourth-order cumulant matrix is established by utilizing the characteristics that the micromotion warhead echo has non-Gaussian characteristic and the cumulant of more than three orders of signals based on multivariate Gaussian distribution is zero, joint diagonalization is carried out, and finally each micromotion warhead echo is separated.

Description

Space micro-motion group target multi-channel blind source separation method
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a spatial micro-motion group target multi-channel blind source separation method.
Background
The flight trajectory of a strategic trajectory missile can be divided into: a boost section, a mid-section, and a reentry section. The boosting section is located in the detectable range of the enemy, the flight time of the reentry section is short, the flight duration of the middle section warhead is long and stable, and the boosting section is used as the optimal stage for detecting the enemy missile. When the missile flies in the middle section, because no atmospheric resistance exists, most baits and fragments formed by explosion of the female bin do rolling motion under the condition of no attitude controller, and only the true warhead with the attitude control and the individual bait warhead do precession or nutation and fly according to a set track. Furthermore, the infrared detection means is substantially ineffective, since in the middle section the infrared radiation capability is substantially lost. The early warning radar has the characteristics of long acting distance, all-time and all-weather, and plays an important role in the aspects of detection, identification, interception, killing evaluation and the like of strategic trajectory missiles.
The group target formed in the middle section area seriously interferes with the operation of a missile defense system, and when the radar detects the mixed echoes of a plurality of targets, the targets are mutually overlapped and inseparable in the time domain and the frequency domain. In order to realize target identification, the echo information of each target must be separated first. The multi-channel blind source separation is relatively comprehensive at present, and can be divided into positive definite blind source separation and underdefinite blind source separation. The positive case indicates that the number of received mixed echoes is equal to the number of group targets, and the negative case indicates that the number of received mixed echoes is less than the number of group targets. For positive and fixed blind source separation, a plurality of radar receiving systems are generally adopted, linear mixed signals of a plurality of targets are respectively received, signal separation is generally carried out by adopting an independent component analysis method, but the method has the problem that the phase, amplitude and separation sequence are different from those of source signals, for target identification, the amplitude problem can be subjected to normalization processing, the separation sequence problem can be ignored, but as the phases of the separated source signals are not all opposite, the separated signals are difficult to uniformly process, and a cushion cannot be laid for subsequent target identification.
Disclosure of Invention
The invention aims to provide a space micro-motion group target multi-channel blind source separation method based on fourth-order cumulant joint diagonalization, and provides a basis for subsequent ballistic missile target identification.
The technical solution for realizing the purpose of the invention is as follows: a spatial micro-motion group target multi-channel blind source separation method comprises the following steps:
step 1, transmitting single frequency pulse to a space micro-motion warhead target to obtain micro-motion complex echoes of a plurality of targets; obtaining a plurality of mixed echoes related to the group target micro warheads by randomly setting a positive and definite mixed matrix, and preprocessing the echoes of the plurality of mixed micro warheads;
step 2, establishing a fourth-order cumulant matrix according to the preprocessed group target micro-motion mixed echoes, performing joint diagonalization, and establishing a target function to minimize the target function;
and 3, establishing a complex Givens rotation matrix, rotating each row and each column in the mixed signal to obtain an optimal unitary matrix, minimizing the objective function to obtain a de-mixing matrix, and reconstructing the echo of each complex micro-motion warhead by using the de-mixing matrix.
Compared with the prior art, the invention has the remarkable advantages that: (1) the invention researches the separation of a plurality of echoes of the aerial micro-motion warhead, establishes a plurality of Givens rotation matrix and can realize the direct separation of a plurality of signals; (2) the invention sets matrix M, combines diagonalization, and compared with the source signal, the separated signal has no problem of opposite phase.
Drawings
FIG. 1 is a schematic flow chart of a spatial micro-motion group target multi-channel blind source separation method based on fourth-order cumulant joint diagonalization.
FIG. 2 is a schematic diagram of a multiple radar reception group target echo system according to the present invention.
FIGS. 3(a) and 3(b) are schematic diagrams of the real part and the imaginary part of each echo complex of the micro-motion target in the invention.
Fig. 4(a) and 4(b) are schematic diagrams of the real part and the imaginary part of the mixed echo of the multi-channel group target of the ballistic missile.
Fig. 5 is a schematic diagram of the separation step of the complex signal of the multi-channel group target mixed echo of the ballistic missile.
FIG. 6 is a schematic representation of the location and size of three missiles of the present invention.
Fig. 7(a), 7(b) are schematic diagrams of real and imaginary parts of normalized target echoes separated by a ballistic group target according to the separation step of fig. 5 in accordance with the present invention.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
With reference to fig. 1, the spatial micro-motion group target multi-channel blind source separation method based on fourth-order cumulant joint diagonalization of the present invention includes the following steps:
step 1, a schematic diagram of a plurality of radar receiving group target echoes is shown in fig. 2, a single frequency pulse with a short time is transmitted to a space micro-motion warhead target, and here, the single frequency pulse with the transmission duration of 3s is selected to obtain a micro-motion complex echo of each target, as shown in fig. 3(a) and 3 (b). By randomly setting a positive mixing matrix, complex mixed echoes about the group target micro warhead are obtained, and as shown in fig. 4(a) and 4(b), the complex mixed micro warhead echoes are preprocessed.
Step 1.1, the echo when the warhead makes micro motion can be converted into the problems of the fixed warhead and the change of the radar line-of-sight angle, and the attitude angle calculation formula of the cone target to the radar wave is found out:
β(t)＝cos-1[cosγcosα-sinγsinαsin(2πt/T)](1)
where β (T) is the attitude angle at time T, α is the radar line-of-sight angle, γ is the motion angle, and T is the motion period.
Suppose that a radar transmits a single-frequency pulse signal for 3s to obtain n warhead micro-motion echoes of si(t),i＝1,...,n。
Step 1.2, randomly setting a mixed matrix with n × n size, multiplying the mixed matrix by a source signal with n dimension to obtain a mixed signal X (t) with n dimension, performing whitening preprocessing on the mixed signal, wherein whitening refers to multiplying the mixed signal X (t) by a whitening matrix V at left side, so that a correlation matrix of the processed signal is an identity matrix, namely:
Figure BDA0002447234260000031
where Z is the preprocessed whitened mixed signal, W is the estimated unmixing matrix, RzA correlation matrix representing the whitened mixed signal.
The covariance matrix of the mixed signal is:
Figure BDA0002447234260000032
where m represents the number of whitened mixed signals, i.e. the number of radar-received mixed echoes.
According to the above formula, RxIs a Hermite matrix that can be decomposed into:
Rx＝QDQT＝QD1/2D1/2QT(4)
wherein Q is RxIs an orthogonal matrix, D ═ diag { λ1,λ2,...,λnIs a diagonal matrix of corresponding eigenvalues, a correlation matrix R of ZZ＝VRxVTThe final whitening matrix is:
V＝D-1/2QT(5)
and 2, a signal separation step is shown in fig. 5, a fourth-order cumulant matrix is established according to the preprocessed group target micro-motion mixed echoes, joint diagonalization is carried out, and an objective function is established to minimize the objective function.
Step 2.1, for the multidimensional complex signal, the fourth-order cumulant is as follows:
Figure BDA0002447234260000041
wherein cum (. cndot.) represents the calculation of the fourth-order cumulant, zi,zj,zk,zlIndicating a whitened mixed signal.
Defining a matrix M of n orders, then obtaining a fourth order cumulant matrix from the whitened mixed signal Z (t), wherein the ith and j elements are:
Figure BDA0002447234260000042
wherein i, j, k, l is 1klIs the k, l-th element of the matrix M.
A fourth order cumulant matrix may be established. Firstly, two vectors i, j are selected to obtain fourth-order cumulant about the ith and jth elements, then the fourth-order cumulant is multiplied by the coefficient of a matrix M, and then the fourth-order cumulant is summed, and all i, j are traversed circularly all the time. The fourth order cumulant equation is as follows:
Figure BDA0002447234260000043
further obtaining:
Figure BDA0002447234260000044
wherein k ispRepresenting the kurtosis, w, of the p-th source signalipIs the ith row, the pth column, m of the unmixing matrix WklIs the ith element of the k row of the matrix M, wpIs the pth column of the unmixing matrix W, and W ═ W1,…,wp,…,wn]And then:
Figure BDA0002447234260000051
step 2.2, singular value decomposition is carried out on the fourth-order cumulant matrix of the formula:
CZ(M)＝WΔ(M)WH(11)
where Δ (M) is the diagonal matrix:
Figure BDA0002447234260000052
for two matrices of order n × n, M1And M2The following can be obtained:
Figure BDA0002447234260000053
then order:
Figure BDA0002447234260000054
wherein Δ ═ Δ (M)1)Δ(M2)-1Is a diagonal matrix, which can be obtained from the above equation:
ΦW＝WΔ (15)
the eigenvalues of phi are the diagonal elements of delta and the eigenvector of phi is W, which is also the whitened mixing matrix W.
Step 2.3, in order to obtain the optimal W, a fourth-order cumulant needs to be obtained from a plurality of M, and n is usually selected2M, then find a unitary matrix W, find the minimum of:
Figure BDA0002447234260000055
where off (-) represents the sum of the squares of all off-diagonal elements.
Cycle through all Mij|i,j＝1,…,nCan obtain n2M, M ═ M11,…,M1n,M21,…,M2n,…,Mn1,…,Mnn]Then n is included in total2×n2＝n4And (4) each element.
And 3, establishing a complex Givens rotation matrix, rotating each row and each column in the mixed signal to obtain an optimal unitary matrix, minimizing the objective function to obtain a de-mixing matrix, and reconstructing the echo of each complex micro-motion warhead by using the de-mixing matrix.
And 3.1, solving the unitary matrix W through Givens rotation. Constructing a complex rotation matrix:
Figure BDA0002447234260000061
wherein, ci,j＝wi,j(1),si,j＝wi,j(2)+iwi,j(3) I is the imaginary partThe unit of (c). And wi,jIs that
Figure BDA0002447234260000062
The feature vector of (2). Then for the whitened hybrid signal z (t) ═ z1(t),z2(t),…,zn(t)]TThe rotation matrix is:
Figure BDA0002447234260000063
the rotation matrix G rotates only the ith and jth row elements of Z (t) at a time, rotating all zi(t) and zj(t), repeating through all i, j, can orthogonalize and normalize the final Z (t).
Step 3.2, the orthogonal normalization matrix W is the product of the rotation matrix G of each time, and each fourth-order cumulant matrix Cz(Mi) And performing joint diagonalization, establishing an objective function, and finding a unitary matrix W which enables the minimum value of the objective function to be the unmixing matrix.
The echo of each micro warhead can be obtained as follows:
Figure BDA0002447234260000064
in order to verify the correctness and validity of the method of the present invention, an example of the spatial micro-motion group target blind source separation is given below. The transmitting frequency is 10GHz, the observation time is 3s, the centroid position of the target 1 is (0, 0, 0), the height is 2.0m, the radius of the bottom surface is 0.35m, the precession is carried out around the Z axis of the coordinate system, the precession period is 1.5s, and the precession angle is 10 degrees; the centroid position of the target 2 is (3, 4, 0), the height is 1.3m, the radius of the bottom surface is 0.33m, precession is carried out around the Z axis of the coordinate system, the precession period is 2.0s, and the precession angle is 8 degrees; the target 3 has a centroid position of (-3, -4, 0), a height of 1.5m, a base radius of 0.30m, precession about the Z axis of the coordinate system with a precession period of 2.7s and a precession angle of 15 °. The target size is shown in fig. 6. Under the condition that the influence caused by translation is not considered, complex echo data about warhead jogging can be obtained by utilizing a region decomposition electromagnetic scattering analysis method of a spherical equivalent source and a target multi-dimensional electromagnetic characteristic evolution mechanism, and a random mixed matrix A is set to be [0.8491,0.7577 and 0.6555; 0.9340,0.7431, 0.1712; 0.6787,0.3922,0.7060], a mixed echo of three channels can be obtained, and real and imaginary parts thereof are shown in fig. 4(a) and 4 (b). The normalized isolated signals obtained by the fourth-order cumulant joint diagonalization are shown in fig. 7(a) and 7 (b). And the error results of the signal separation are as follows:
TABLE 1
Degree of similarity Relative root mean square error
Target
1 electric field 99.93％ 4.48％
Target
2 electric field 99.96％ 2.91％
Target
3 electric field 99.98％ 3.57％
As can be seen from Table 1, the separation errors of the three targets are all below 5%, the separation errors are very close to the source signals, the similarity is all above 99.9%, and the waveform goodness of fit is extremely high.
In conclusion, according to the invention, the four-order cumulant matrix of the whitened mixed signal is established by utilizing the non-Gaussian characteristic of the echo of the micro-motion warhead in the air, wherein the cumulant of more than three orders of Gaussian signals is zero and the non-Gaussian characteristic of the echo of the micro-motion warhead is fully utilized. And performing joint approximate diagonalization on the established fourth-order cumulant matrix to establish an objective function, and solving a mixed matrix which enables non-diagonal elements of the objective function to be the minimum by establishing a Givens rotation matrix. The problem of direct separation of the micro-motion warhead complex mixed signal and the problem that the phase of the separated echo is not opposite to that of the echo of a real micro-motion target are solved.

Claims (5)

1. A space micro-motion group target multi-channel blind source separation method is characterized by comprising the following steps:
step 1, transmitting single frequency pulse to a space micro-motion warhead target to obtain micro-motion complex echoes of a plurality of targets; obtaining a plurality of mixed echoes related to the group target micro warheads by randomly setting a positive and definite mixed matrix, and preprocessing the echoes of the plurality of mixed micro warheads;
step 2, establishing a fourth-order cumulant matrix according to the preprocessed group target micro-motion mixed echoes, performing joint diagonalization, and establishing a target function to minimize the target function;
and 3, establishing a complex Givens rotation matrix, rotating each row and each column in the mixed signal to obtain an optimal unitary matrix, minimizing the objective function to obtain a de-mixing matrix, and reconstructing the echo of each complex micro-motion warhead by using the de-mixing matrix.
2. The spatial micro-motion group target multi-channel blind source separation method as claimed in claim 1, wherein the duration of the single frequency pulse transmitted to the spatial micro-motion warhead target in step 1 is 3 s.
3. The spatial micro-motion group target multi-channel blind source separation method according to claim 2, wherein the specific method in step 1 is as follows:
step 1.1, the echo when the warhead makes micro motion can be converted into the problems of the fixed warhead and the change of the radar line-of-sight angle, and the attitude angle calculation formula of the cone target to the radar wave is found out:
β(t)＝cos-1[cosγcosα-sinγsinαsin(2πt/T)](1)
wherein β (T) is the attitude angle at time T, α is the radar line-of-sight angle, gamma is the motion angle, and T is the motion period;
suppose that a radar transmits a single-frequency pulse signal for 3s to obtain n warhead micro-motion echoes of si(t),i＝1,...,n；
Step 1.2, randomly setting a mixed matrix with n × n size, multiplying the mixed matrix by a source signal with n dimension to obtain a mixed signal X (t) with n dimension, performing whitening preprocessing on the mixed signal, wherein whitening refers to multiplying the mixed signal X (t) by a whitening matrix V at left side, so that a correlation matrix of the processed signal is an identity matrix, namely:
Figure FDA0002447234250000011
where Z is the preprocessed whitened mixed signal, W is the estimated unmixing matrix, RzA correlation matrix representing the whitened mixed signal;
the covariance matrix of the mixed signal is:
Figure FDA0002447234250000021
wherein m represents the number of whitened mixed signals, namely the number of radar-received mixed echoes;
according to the above formula, RxIs a Hermite matrix that can be decomposed into:
Rx＝QDQT＝QD1/2D1/2QT(4)
wherein Q is RxIs an orthogonal matrix, D ═ diag { λ1,λ2,...,λnIs a diagonal matrix of corresponding eigenvalues, a correlation matrix R of ZZ＝VRxVTThe final whitening matrix is:
V＝D-1/2QT(5) 。
4. the spatial micro-motion group target multi-channel blind source separation method according to claim 1, wherein the step 2 is to establish a fourth-order cumulant matrix according to the preprocessed group target micro-motion mixed echoes, and perform joint diagonalization to establish an objective function so as to minimize the objective function, and specifically comprises the following steps:
step 2.1, for the multidimensional complex signal, the fourth-order cumulant is as follows:
Figure FDA0002447234250000022
wherein cum (. cndot.) represents the calculation of the fourth-order cumulant, zi,zj,zk,zlRepresenting a certain whitened mixed signal;
defining a matrix M of n orders, then obtaining a fourth order cumulant matrix from the whitened mixed signal Z (t), wherein the ith and j elements are:
Figure FDA0002447234250000023
wherein i, j, k, l is 1klIs the kth, l element of the matrix M;
a fourth order cumulant matrix may thus be established; firstly, selecting two vectors i, j to obtain fourth-order cumulant about the ith and j elements, then multiplying the fourth-order cumulant by the coefficient of a matrix M, then summing, and circularly traversing all i, j all the time; the fourth order cumulant equation is as follows:
Figure FDA0002447234250000031
further obtaining:
Figure FDA0002447234250000032
wherein k ispRepresenting the kurtosis, w, of the p-th source signalipIs the ith row of the unmixing matrix Wp columns, mklIs the ith element of the k row of the matrix M, wpIs the pth column of the unmixing matrix W, and W ═ W1,…,wp,…,wn]And then:
Figure FDA0002447234250000033
step 2.2, singular value decomposition is carried out on the fourth-order cumulant matrix of the formula:
CZ(M)＝WΔ(M)WH(11)
where Δ (M) is the diagonal matrix:
Figure FDA0002447234250000034
for two matrices of order n × n, M1And M2The following can be obtained:
Figure FDA0002447234250000035
then order:
Figure FDA0002447234250000036
wherein Δ ═ Δ (M)1)Δ(M2)-1Is a diagonal matrix, which can be obtained from the above equation:
ΦW＝WΔ (15)
the eigenvalue of phi is the diagonal element of delta, and the eigenvector of phi is W, and is also the whitened mixing matrix W;
step 2.3, in order to obtain the optimal W, four-order cumulant needs to be obtained for a plurality of M, and n is selected2M, then find a unitary matrix W, find the minimum of:
Figure FDA0002447234250000041
where off (-) represents the sum of the squares of all off-diagonal elements;
cycle through all Mij|i,j＝1,…,nObtaining n2M, M ═ M11,…,M1n,M21,…,M2n,…,Mn1,…,Mnn]Then n is included in total2×n2＝n4And (4) each element.
5. The spatial micro-motion group target multi-channel blind source separation method according to claim 1, wherein the step 3 establishes a complex Givens rotation matrix, rotates each row and each column in the mixed signal to obtain an optimal unitary matrix, minimizes an objective function, thereby obtaining a unmixing matrix, and reconstructs an echo of each complex micro-motion warhead by using the unmixing matrix, which is specifically as follows:
step 3.1, solving the unitary matrix W through Givens rotation, and constructing a complex rotation matrix:
Figure FDA0002447234250000042
wherein, ci,j＝wi,j(1),si,j＝wi,j(2)+iwi,j(3) I is the unit of the imaginary part; and wi,jIs that
Figure FDA0002447234250000043
The feature vector of (2); then for the whitened hybrid signal z (t) ═ z1(t),z2(t),…,zn(t)]TThe rotation matrix is:
Figure FDA0002447234250000044
the rotation matrix G rotates only the ith and jth row elements of Z (t) at a time, rotating all zi(t) and zj(t) repeating the traversal of all i, j, orthogonalizing and normalizing the final z (t);
step 3.2, the orthonormal matrix W is the product of every rotation matrix GFor each fourth order cumulant matrix Cz(Mi) Performing joint diagonalization, establishing a target function, and finding a unitary matrix W which enables the minimum value of the target function to be the unmixing matrix;
the echo of each micro warhead can be obtained as follows:
Figure FDA0002447234250000051
。
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